P8901 [USACO22DEC] Circular Barn S

合集 - 博弈(8)

1.B. Coin Games2024-05-142.C. Swap Game2024-05-153.A. Jellyfish and Game2024-05-15

4.P8901 [USACO22DEC] Circular Barn S2024-06-08

5.D. World is Mine2024-07-026.C. Salyg1n and the MEX Game2024-07-217.C. Game on Permutation2024-07-218.P10838 『FLA - I』庭中有奇树2024-08-07

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原题链接

题解

真tm麻烦

先考虑只有一个数的情况

假如我是后手，由于每次可以减123，无论对手减多少，我总可以使这一轮这个数总共减去的值为四的倍数
恰好当n位4的时候先手必败，所以如果一个数为四的倍数时，先手必败

考虑多个数

数组里，有的数是4的倍数，有的不是。
此时假设我是先手，遇到四的倍数，我要尽可能地减慢这个数变小的速度，对于非四倍数的数，我要尽可能加快变小的速度

code

#include <bits/stdc++.h>
using namespace std;

const int MAX_N = 100005;
const int MAX_P = 5000035;
const int MAX_V = 5000006;

int nums[MAX_N];
int primes[MAX_P];
int isComp[MAX_P] = {0};
int pCount = 1;
vector<int> pMod1, pMod2, pMod3;

void sieve() {
    primes[1] = 1;
    for (int i = 2; i <= MAX_V; i++) {
        if (!isComp[i]) {
            primes[++pCount] = i;
            if (i % 4 == 1) pMod1.push_back(i);
            if (i % 4 == 2) pMod2.push_back(i);
            if (i % 4 == 3) pMod3.push_back(i);
        }
        for (int j = 2; j <= pCount; j++) {
            if (primes[j] * i >= MAX_V) break;
            isComp[i * primes[j]] = 1;
            if (i % primes[j] == 0) break;
        }
    }
}

int main() {
    sieve();
    
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        for (int i = 1; i <= n; i++) cin >> nums[i];
        
        int minStepsNhoj = INT_MAX, minStepsJohn = INT_MAX;
        int minIdxNhoj = -1, minIdxJohn = -1;
        
        for (int i = 1; i <= n; i++) {
            int num = nums[i];
            if (num % 4 == 0) {
                int steps = num / 4 + 1;
                if (steps < minStepsNhoj) {
                    minStepsNhoj = steps;
                    minIdxNhoj = i;
                }
            } else if (num % 4 == 1) {
                auto upper = upper_bound(pMod1.begin(), pMod1.end(), num);
                if (upper != pMod1.end()) {
                    int steps = (num - *(upper - 1)) / 4 + 1;
                    if (steps < minStepsJohn) {
                        minStepsJohn = steps;
                        minIdxJohn = i;
                    }
                }
            } else if (num % 4 == 2) {
                auto upper = upper_bound(pMod2.begin(), pMod2.end(), num);
                if (upper != pMod2.end()) {
                    int steps = (num - *(upper - 1)) / 4 + 1;
                    if (steps < minStepsJohn) {
                        minStepsJohn = steps;
                        minIdxJohn = i;
                    }
                }
            } else if (num % 4 == 3) {
                auto upper = upper_bound(pMod3.begin(), pMod3.end(), num);
                if (upper != pMod3.end()) {
                    int steps = (num - *(upper - 1)) / 4 + 1;
                    if (steps < minStepsJohn) {
                        minStepsJohn = steps;
                        minIdxJohn = i;
                    }
                }
            }
        }
        
        if (minStepsNhoj < minStepsJohn) {
            puts("Farmer Nhoj");
        } else if (minStepsNhoj > minStepsJohn) {
            puts("Farmer John");
        } else if (minIdxNhoj < minIdxJohn) {
            puts("Farmer Nhoj");
        } else {
            puts("Farmer John");
        }
    }
    return 0;
}